Pupils at Haverstock school, in Camden, north London, have spent nearly a month being taught in sports halls and community centres after contractors overran two deadlines.
Last year Mr Miliband predicted: "We confidently expect that Haverstock school will be delivered on time and on budget. Children's education depends on high-quality buildings."
Builders Kajima had agreed to finish most of the school in time for lessons to start on September 13, but admitted at a late stage that they were behind schedule.
Even with teachers working through the weekend to set up classrooms, another start date, fixed for last Monday, was also missed.
Pupils have been taught a cut-down curriculum of English, maths, humanities and ICT in nearby council buildings.
Kajima has been fined an undisclosed sum for the delay and Camden council will not pay for the school until it is occupied.
Julian Rudd-Jones, a director of Kajima, said: "That doesn't make up for the fact that kids have suffered for a few weeks. We are sorry, but we can't undo what's done."
He said the delay, blamed on bad weather and a constricted site, could have happened on any building job, and was nothing to do with it being a PFI scheme.
Similar projects for dozens of schools in places such as Wirral, Kirklees and Brighton and Hove had suffered months of delays.
John Dowd, the school's headteacher, said: "I am confident we will be able to make up any detrimental effects over the course of the school year. In the long term, all our pupils will benefit immensely from the school's transformation."
Construction began last summer, after the school's 14 Victorian buildings had been declared unfit for purpose. The new 70-classroom school will feature a floodlit all-weather sports pitch and basketball courts.
Mr Miliband was unavailable for comment. A Department for Education and Skills spokeswoman said: "As in all PFI contracts, if costs overrun, or if a school building is not delivered on time, the private-sector partner and its shareholders bear the financial consequences."